Thermodynamics of the ferromagnetic phase transition in nearly half metallic CoS2 at high pressures

Ames Laboratory Publications

Ames Laboratory

3-2014

Thermodynamics of the ferromagnetic phase

transition in nearly half metallic CoS2 at high

pressures

F. S. Elkin

Russian Academy of Sciences

I. P. Zibrov

Russian Academy of Sciences

A. P. Novikov

Russian Academy of Sciences

S. S. Khasanov

Russian Academy of Sciences

V. A. Sidorov

Russian Academy of Sciences

See next page for additional authors

Follow this and additional works at:

https://lib.dr.iastate.edu/ameslab_pubs

Part of the

Condensed Matter Physics Commons

,

Engineering Physics Commons

, and the

Metallurgy Commons

The complete bibliographic information for this item can be found at

https://lib.dr.iastate.edu/

ameslab_pubs/423

. For information on how to cite this item, please visit

http://lib.dr.iastate.edu/

howtocite.html

.

Thermodynamics of the ferromagnetic phase transition in nearly half

metallic CoS2 at high pressures

Abstract

The volume change and heat capacity at the ferromagnetic phase transition in CoS2 were measured at high

pressures using X-rays generated by the Argonne synchrotron light source and by ac-calorimetry, respectively.

The transition entropy, calculated on the basis of these experimental data, drops along the transition line due

to quantum degradation, as required by Nernst's law. The volume change increases strongly along the

transition line, which is explained by specifics of the compressibility difference of coexisting phases that

results from nearly half metallic nature of the ferromagnetic phase of CoS2.

Keywords

A. Half-metal, D. Phase transition, E. X-ray, E. Specific heat

Disciplines

Condensed Matter Physics | Engineering Physics | Materials Science and Engineering | Metallurgy

Comments

This is a manuscript of the article published as Elkin, F. S., I. P. Zibrov, A. P. Novikov, S. S. Khasanov, V. A.

Sidorov, A. E. Petrova, Thomas A. Lograsso, J. D. Thompson, and S. M. Stishov. "Thermodynamics of the

ferromagnetic phase transition in nearly half metallic CoS2 at high pressures."

Solid State Communications

181

(2014): 41-45. DOI:

10.1016/j.ssc.2013.12.001

. Posted with permission.

Creative Commons License

This work is licensed under a

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0

License

.

Authors

F. S. Elkin, I. P. Zibrov, A. P. Novikov, S. S. Khasanov, V. A. Sidorov, A. E. Petrova, Thomas A. Lograsso, J. D.

Thompson, and S. M. Stishov

arXiv:1310.3994v1 [cond-mat.str-el] 15 Oct 2013

Thermodynamics of the ferromagnetic phase

transition in nearly half metallic CoS

at high

pressures

F S Elkin1

, I P Zibrov1

, A P Novikov1

, S S Khasanov2 , V A Sidorov1

, A E Petrova1

, T A Lograsso3

, J D Thompson4

, S.M. Stishov1

1

Institute for High Pressure Physics of Russian Academy of Sciences, Troitsk, Russia

2

Institute for Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, Russia

3

Ames Laboratory, Iowa State University, Ames, IA 50011, USA

4

Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]

PACS numbers: 62.50.-p, 75.30.Kz, 75.40.Cx

Abstract. The volume change and heat capacity at the ferromagnetic phase transition in CoS2 were measured at high pressures using X-rays generated by

the Argonne synchrotron light source and by ac-calorimetry, respectively. The transition entropy, calculated on the basis of these experimental data, drops along the transition line due to quantum degradation, as required by Nernst’s law. The volume change increases strongly along the transition line, which is explained by specifics of the compressibility difference of coexisting phases that results from nearly half metallic nature of the ferromagnetic phase of CoS2.

1. Introduction

Cobalt disulphide, CoS2, a metallic compound with the cubic pyrite-type crystal

structure [1], exhibits a phase transition to a ferromagnetic state atTc ∼122 K Ref. [2]

that magnetic and electric properties indicate to be itinerant in nature [2, 3, 4, 5, 6]. Upon entering the ferromagnetic state CoS2 becomes a nearly half metal with a

significant decrease in the density of states at the Fermi level that is reflected in an increase in the resistivity below Tc [7, 8]. The temperature-pressure phase

diagram of CoS2 has been studied to high pressures where experiments show that

the ferromagnetic transition decreases monotonically and trends to zero at ∼6 GPa [9, 10, 11, 12]. A change from continuous to first-order phase transition with a tricritical point close to ambient pressure was suggested in Refs. [11, 12], which accounts for the absence of a non-Fermi liquid temperature dependence of the resistivity near this critical pressure [12]. The conclusion for a strong first-order quantum-phase transition in CoS2was based on indirect arguments [12]; consequently,

2. Experimental

We report an X-ray study of the lattice parameter change at the phase transition in CoS2 along the pressure-dependent transition line. Single crystals of CoS2 were

grown by chemical-vapor-transport [12], and some crystals were ground in an agate mortar to prepare a powder sample. X-ray diffraction studies of both crystals and powders of CoS2 were performed at the HPCAT (16BM-D) beam line of the

Advanced Photon Source (APS), Argonne National Laboratory. Single-crystal data were collected using the rotation method (ω-axis rotation rate of±17◦_{/500 sec, X-ray}

wave lengthλ= 0.424603˚A) and unit-cell parameters were calculated from the (610) and (440) reflections. In the powder-diffraction experiments, the X-ray wave length

λ= 0.354300˚Awas chosen to get the ten strongest reflections. In both experiments, an image plate detector MAR345, calibrated with fine CeO2 standard powder, was

used for data collection. Examples of the diffraction patterns are given in Fig. 1. The collected data were subjected to the full profile analysis using the GSAS software package [13, 14], with a resulting accuracy of the unit-cell parameter determination of

±1×10−4_˚ A.

For the diffraction experiments, high pressures were generated in a diamond anvil cell with ∼400µm culet diameters and∼60◦ _{aperture. A 200µm hole was drilled}

in the pre-indented stainless-steel gasket. A powder or single crystal sample of CoS2

(∼50×50×10µm3

in size) and ruby chips were placed in the sample chamber that was filled with helium to a pressure of∼200 MPa. A gas-membrane device equipped with a pressure-control system was employed to pressure-load the cell. For these experiments, the cell was attached to a cold-finger type cryostat, which provided temperatures down to 15 K measured by a Cernox thermometer. Pressure was measured by the ruby luminescence technique with accuracy±2×10−5_{GPa making use of the standard ruby}

calibration scale and with the appropriate temperature correction, in correspondence with procedures accepted in the HPCAT.

27.3 27.4 27.5

20 40 60 80 100

Ferro

Para 5.8 GPa

5.6 GPa

I

n

t

e

n

s

i

t

y

(

a

r

b

.

u

n

i

t

s

)

2 (deg)

4.13 GPa 6.33 GPa

T=23K (610)

Figure 1. (Color online) Position of (601) reflection from a single crystal of CoS2as a function of pressure at 23 K. Reflection shift between 5.6 and 5.8 GPa

corresponds to the first order phase transition.

Phase transition in CoS2 at high pressures 3

cell [16] with a glycerol/water (3:2 by volume) mixture as the pressure medium. Pressure at low temperatures was estimated from the superconducting transition temperature of lead [17].

3. Results

Figure 2 gives typical results for the variation in unit-cell volume around the phase boundary. Experimental conditions, unfortunately, introduce sufficient error in accurately determining the pressure and temperature that it is not possible to distinguish in these data the difference between a continuous phase transition and a jump inherent to a first-order phase transition. We take the change in cell volume at the phase transition to be given by the dashed curves in Fig. 2. Consequently, it is not possible to draw conclusions from these data about the tricritical behavior in CoS2 (Ref. [11, 12]). On the other hand, these experimental uncertainties are

inconsequential in determining the isothermal change in cell volume as a function of pressure in the high pressure regime that is plotted in Fig. 3. In the next section, results of Figs. 2 and 3 will be compared to heat capacity data plotted in Fig. 4. These data demonstrate an evolution of the phase-transition heat with temperature and pressure. The initial rise of the heat capacity peak with increasing pressure probably signifies the crossover from second to first order transitions. The pressure dependence of the phase-transition temperature deduced from the current experimental data is shown in Fig. 5. As seen, the phase line obtained from X-ray diffraction differs significantly from that determined from electrical resistivity, susceptibility and heat capacity data [12]. Obviously, calibrations of the low temperature ruby pressure scale and the scale based on the superconducting transition temperature of lead greatly disagree. It is worth noting that the phase-transition line in CoS2 that also had been established

in Ref. [10, 12] with use the ”lead” high pressure scale also differs from the current data probably due to non hydrostatic experimental conditions. Figures 6 and 7 summarize the pressure-dependent evolution of ∆V and ∆V /VF along the transition

line. Here ∆V =VP−VF, whereVP andVF are the unit-cell volume calculated from

lattice-parameter data in the paramagnetic and ferromagnetic phases, respectively. We emphasize a special behavior of ∆V: its absolute value|∆V|increases with pressure, which probably indicates involvement of some nontrivial physics. Despite an increase of ∆V by an order of magnitude in the range from 120 to 20K, the maximum ratio ∆V /VF reaches only∼0.1 percent, so there is not a strong first order phase transition

in CoS2 at high pressure.

The presented data permit calculations of the entropy of the phase transition in CoS2. Two sets of calculations are presented in Fig. 8. Set 1 is calculated from the

volume change at the phase transition (Fig. 6) together with the Clausius-Clapeyron equation dT /dP = ∆V /∆S, which connects the slope of the transition curve with a difference of volume and entropy. Set 2 was obtained by integrating the heat capacity data (Fig. 4). Both curves in Fig. 8 qualitatively agree, reflecting a fast quantum degradation of the transition entropy with lowering temperature from temperatures as high as 110 K. The quantitative difference between the two sets is attributed to many factors, including uncertainty in the heat capacity of CoS2 due to inadequate

20 40 60 80 100 120 140 160 165.8

165.9 166.0 166.1 166.2 166.3

Powder

V

o

l

u

m

e

(

A

3

)

2.1GPa

20 40 60 80 100 120 140 160

165.7 165.8 165.9 166.0 166.1 166.2

V

o

l

u

m

e

(

A

3

)

Single crystal 2.24GPa

20 40 60 80 100 120 140 160

163.1 163.2 163.3 163.4 163.5 163.6

V

o

l

u

m

e

(

A

3

)

Single crystal 4.15GPa

Temperature (K)

Figure 2. (Color online) Examples of the temperature dependence of the unit-cell volume of CoS2in the vicinity of its ferromagnetic phase transition. Dashed curves

are guides to the eye. It is tempting to ascribe the seemingly two anomalies at the phase transition shown in the middle panel to a splitting of the phase transition; however, heat capacity data do not support this supposition.

4. Discussion

As seen from the experimental data, there is a steep growth of the volume change with pressure at the ferromagnetic phase transition in CoS2. This behavior could

be connected at least partly with the tricritical crossover supposedly observed in CoS2 at its magnetic phase transition close to ambient pressure [11, 12]. In this

case, first order features should grow on compression, which is in fair agreement with the general evolution of ∆V. On the other hand, a negative volume change at a phase transition, such as seen in CoS2, is typical of itinerant magnets and is a

manifestation of a magnetovolume effect or volume magnetostriction [20]. Neglecting the spin fluctuations, the volume change due to band polarization and associated spontaneous magnetization can be written as [21, 22]

∆V /VF = (C/K)M

Phase transition in CoS2 at high pressures 5

4.0 4.5 5.0 5.5 6.0 6.5

160.5 161.0 161.5 162.0 162.5 163.0 163.5 164.0 5.8 GPa V o l u m e ( A 3 ) Pressure (GPa) T=23K 5.6 GPa

Figure 3. (Color online) Compression isotherm of CoS2. As shown by the

discontinuity in these data, a first order phase transition occurs between 5.6 and 5.8 GPa. Error bars correspond to the circle size.

60 70 80 90 100 110 120 130

0 1 2 3 4 0 1 2 3

60 70 80 90

0.0 0.1 0.2 1.22 0 C m a g / T ( J/ K 2 ) Temperature (K) C m a g / T ( J/ m o l -K 2 ) 4.24 3.88 3.39 2.34 C m a g / T ( J/ K 2 ) 4.24 3.88 3.39

Figure 4. (Color online) Heat capacity of CoS2 in the vicinity of its phase

transition. Numbers above the peaks correspond to pressure values in GPa. In the inset the heat capacity peaks at 3.39, 3.88 and 4.24 GPa are shown in the enlarged scale

where M is the magnetization, K is the bulk modulus, and C is the magnetovolume coupling constant. As seen in Fig. 7, ∆V /VF changes by an order of magnitude

along the transition line. To explain this observation, the magnetization M of the ferromagnetic phase CoS2 at the transition line should increase considerably

0 1 2 3 4 5 6 0

20 40 60 80 100 120

single crystal powder powder (Ref. 18)

T

c

(

K

)

Pressure (GPa) 1

2

Figure 5. (Color online) Phase diagram of CoS2 at high pressure. Curve 1 was

determined making use a ”lead” manometer to measure pressure [12]. Curve 2 was determined by X-ray diffraction and the pressure measured by a ruby sensor.

0 1 2 3 4 5 6

-0.15 -0.10 -0.05 0.00

single crystal

powder

Ref .

12

V

(

A

3

)

Pressure (GPa)

Figure 6. (Color online) Volume change at the ferromagnetic phase transition in single crystal and powder samples of CoS2as a function of pressure. The dashed

curve is a guide to the eyes.

and paramagnetic phases [25]. But, the nearly half metal nature of the ferromagnetic phase of CoS2 creates a new situation. The point is that most of the electrons of

the minority band become localized in the nearly half metallic state. This influences the repulsive interaction between electrons in CoS2 in such a way to decrease the

compressibility. An analogous situation is realized in a high pressure study of the model half-metal CrO2 [26]. This conclusion is supported by the pressure-dependent

Phase transition in CoS2 at high pressures 7

0 1 2 3 4 5 6

-8 -6 -4 -2 0

V

/

V

(

1

0

-4

)

Powder

Single crystal

Ref.

12

Pressure (GPa)

Figure 7. (Color online) Relative volume change at the ferromagnetic phase transition in CoS2 as a function of pressure. The dashed curve is a guide to the

eyes.

20 40 60 80 100 120

0.0 0.1 0.2 0.3 0.4 0.5

S

/

(

R

l

n

2

)

Temperature (K) 1

2

4 3

Figure 8. (Color online) Entropy of the phase transition in CoS2as a function of

temperature. Symbols denote the entropy measured at the phase transition and dashed curves are guides. Curve1: entropy change calculated from the Clapeyron-Clausius equation; curve 2: entropy change calculated from heat capacity data (Fig. 4); point 3: calorimetry result at ambient pressure [19]; point 4: calculated from dilatometric measurements at ambient pressure [12]. Pressure measurements in experiments leading to curves 1 and 2 were based on different pressure scales (Fig. 5). To compare these results on an equal footing, they were plotted as functions of temperature.

metallic states. Note that at higher temperatures the corresponding jumps increase significantly ((Fig. 10b) that may imply decreasing half metallicity with pressure if the phonon and magnon contributions can be neglected.

4 5 6 7 6.8

7.0 7.2 7.4 7.6 7.8

T=23 K

C

o

m

p

r

e

s

s

i

b

i

l

i

t

y

(

1

0

-3

/

G

P

a

)

Pressure (GPa)

FM PM

Figure 9. Compressibility discontinuity at the phase transition in CoS2at high

pressure, calculated from the compression isotherm (Fig. 3). The compressibility of paramagnetic phase exceeds that of the ferromagnetic phase.

the current observation [27]. In the Landau theory, however, only anomalous parts of thermodynamic quantities are considered; whereas, the regular background contributions, which could drastically change at a phase transition, cannot be treated in a general way. In CoS2, the sign of the compressibility change is certainly defined

by the background, which eliminates a contradiction with the Landau theory.

5. Conclusion

The volume change and heat capacity were measured at the ferromagnetic phase transition in CoS2 at high pressure, and the transition entropy was calculated from

these experimental data. The transition entropy drops along the transition line due to quantum degradation, as required by the Nernst law. The volume change increases substantially along the transition line and is explained by specifics of the compressibility difference of the coexisting phases, which results from the nearly half metallic nature of the ferromagnetic phase of CoS2.

Acknowledgments

Phase transition in CoS2 at high pressures 9

2 3 4 5 6

1.4 1.6 1.8 2.0 2.2 2.4 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0 20 40 60 80 T = 1.28 K

T = 60 K

C / T ( J/ K 2 ) Pressure (GPa) a) C / T ( J/ K 2 )

0 20 40 60 80

0.00 0.02 0.04 0.06 0.08 0.10 C / T C ( J/ K 2 ) T C (K) b) C / T C ( m J/ m o l -K 2 )

Figure 10. a) Jumps of heat capacity divided by temperature at the phase transition in CoS2 at T=1.28 K and T= 60 K. Values of Cp/T correspond

to heat capacity of the sample plus uncertain amount of pressure transmitting media. Heat capacity of the media stays constant at the phase transition therefore providing a possibility to calculate an absolute value of ∆Cp/T, as shown in the

figure. Note that the jump at 60 K is much higher than at 1.28 K b) Jumps of heat capacity divided by temperature at the phase transition in CoS2 as a

function of transition temperatureTc. Heat capacity of the media stays constant

at the phase transition therefore providing a possibility to calculate an absolute value of ∆Cp/T, as shown in the figure.

is supported by DOE-BES, under Contract No. DE-AC02-06CH11357. F.E and I.Z greatly appreciate help of C. Kenney-Benson, D. Ikuta and D.Popov.

References

[1] Elliot N 1960J. Chem. Phys.33903

[2] Jarrett H S, Cloud W H, Bouchard R J, Butler S R, Frederick C G, Gillson J L 1968Phys. Rev. Lett.21617

[3] Adachi K, Sato K, Takeda M 1969J. Phys. Soc. Japan26631 [4] Ogawa S, Waki S, Teranishi T 1974Int. J. Magnetism5349 [5] Adachi K, Ohkohchi K 1980J. Phys. Soc. Japan 49154 [6] Hiraki H, Endoh Y, Yamada K 1997J. Phys. Soc. Japan66818 [7] Yomo S 1979J. Phys. Soc. Japan471486

[8] Hiraka H, Endoh Y 1996J. Phys. Soc. Japan653740

[10] Barakat S, Braithwaite D, Alireza P, Grube K, Uhlarz M, Wilson J, Pfleiderer C, Flouquet J, Lonzarich G 2005Physica B 359-3611216

[11] Otero-Leal M, Rivadulla F, Garc´ıa-Hern´andez M, Pi˜neiro A, Pardo V, Baldomir D, Rivas J 2008

Phys. Rev. B 78180415(R)

[12] Sidorov V A, Krasnorusski V N, Petrova A E, Utyuzh A N, Yuhasz W M, Lograsso T A, Thompson J D, Stishov S M 2011Phys.Rev. B83060412 (R)

[13] Larson A C, Von Dreele R B 1987 General Structure Analysis System (GSAS), Los Alamos National Laboratory, 2000, Report LAUR 86-748

[14] Toby B H 2001J. Appl. Crystallogr.34210

[15] Sidorov V A, Thompson J D, Fisk Z 2010J. Phys.: Condens. Matter 22406002 [16] Petrova A E, Sidorov V A, Stishov S M 2005Physica B359-3611463

[17] Eiling A, Schilling J S 1981J. Phys. F: Met. Phys.11623

[18] Machida A, Synchrotron Radiation Research Center, Japan (unpublished) [19] Ogawa S 1976J.Phys. Soc. Japan41462

[20] Mohn P,Magnetism in the Solid State, An Introduction(Springer) [21] Moria T, Usami K 1980Solid State Comm.3495

[22] Shiga M 1981J.Phys. Soc. Japan 502573

[23] Mushnikov N V, Goto T, Andreev A V, Zadvorkin S M 2000Phil. Mag. B8081 [24] Liu X B, Altounian Z 2007J. Appl. Phys.10109G511

[25] Petrova A E, Stishov S M 2009J. Phys.: Condens. Matter 21196001